Question

Resolve each of the following quadratic trinomials into factors:

3x² + 22x + 35

Answer 1

3x² + 22x + 35

Here, coefficient of x² = 3, coefficient of x = 22 and constant term = 35

We shall now split up the coefficient of x i.e., 22 into two parts whose sum is 22 and product is 3 x 35 = 105

So, we write middle term 22x as 15x + 7x

Thus, we have

3x² + 22x + 35 = 3x² + 15x + 7x + 35

= 3x (x + 5) + 7 (x + 5)

= (3x + 7) (x+ 5)